Problem: Solve for $x$ and $y$ using elimination. ${4x-y = 18}$ ${5x+y = 45}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $9x = 63$ $\dfrac{9x}{{9}} = \dfrac{63}{{9}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {4x-y = 18}\thinspace$ to find $y$ ${4}{(7)}{ - y = 18}$ $28-y = 18$ $28{-28} - y = 18{-28}$ $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {5x+y = 45}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ + y = 45}$ ${y = 10}$